Implicit Sampling

The need to sample complicated many-dimensional probability densities arises in applications ranging from data analysis to computational physics. This typically requires that a suitable importance density be found, which can be difficult. Implicit sampling is a general algorithm for finding effective importance densities; generality is achieved by not requiring that the densities be known explicitly, with samples found by solving an algebraic equation for each sample.

Multiphysics in Materials and Industrial Devices

The Voronoi Implicit Interface Method (VIIM) was used to compute complex multiphase
physics problems, including the evolution of interfaces under surface tension,
geometry constraints (such as enclosed and target volumes), as well as underlying
physics. Coupling to a full projection Navier-Stokes solver allows computation of
fluid flow and interface forces.

Simulation of Vertical-Axis Wind Turbines

Vertical axis wind turbines (VAWT), in which the main rotor shaft is set vertically, have many advantages, including the fact they do not need to be pointed into the wind. Optimizing blade design and structure is highly challenging. We were able to accurately compute optimal VAWT configurations in various environments.

Rolling Tires and Failure

The process of fracture in tires is a complex problem in polymer chemistry, materials science, and mechanics. In order to effectively predict the state of balance for design purposes, one needs a methodology for computing the internal stress state in the tire. At its most elementary level, one needs to solve the nonlinear equations of elasticity and, in more complex cases, those of viscoelastic solids.

About the Group

The Mathematics Group at LBNL develops new mathematical models, devises new algorithms, explores new applications, exports key technologies, and trains young scientists in support of DOE. We use mathematical tools from a variety of areas in mathematics, physics, statistics, and computer science, including statistical physics, differential geometry, asymptotics, graph theory, partial differential equations, discrete mathematics, and combinatorics. The problems we attack are both technologically interesting and mathematically challenging, and form a set of interrelated computing methodologies and applications in support of the DOE energy mission.

One set of topics focuses on optimizing the manufacture and operation of engineering and industrial processes. Applications include semiconductors, coating rollers, inkjet printing technologies and microfluid effects, foams in manufacturing processes, new metals, granular mixers, coal hoppers, rolling tires, mode-locked lasers, wind turbines, vibrating RF MEMS devices for wireless communications, and dynamic fracture in bulk metallic glasses. Another set of topics focuses on tools for the analysis of energy processes, and includes stochastic methods in environmental science, data analysis for meteorological data, data synthesis for wind energy and large-scale ocean currents, seismic imaging, image processing and analysis for analyzing cellular structures, and complex fluid-membrane solvers for understanding the dynamics behind cellular development in new biofuels. and path planning for determining chemical accessibility in new materials such as zeolite and metal organic frameworks for gas separation sieves in carbon sequestration.

Tackling these problems with enough accuracy to be useful requires some of the most advanced computational resources. To that end, part of our work is aimed at developing the mathematics behind higher order accurate algorithms that naturally lend themselves to new architectures, where attention to communication, data exchange, and decompositions offer the opportunity for tremendous speedup.

Our program consists of faculty, postdocs, graduate students, and visitors. The four principal investigators (Chorin, Persson, Sethian, and Wilkening) are all faculty at UC Berkeley. However, the close proximity of LBNL to campus and the far greater wealth of resources at LBNL makes it the attractive center of applied computational mathematics at Berkeley. This is reflected in the fact that all the graduate students, postdocs and faculty have a shared seminar space and offices. Together with the presence of NERSC and other computational resources, this makes LBNL a natural focal point and magnet.